I am trying to use the advanced setting TIME_DISP_START_DATE and nothing seems to be happening.
According to the tool tip, this advanced setting "shows first day of month/week instead of month/week number." I'm using the Google Analytics data source and I've tried all of the week related time dimensions.
I see in the screenshot that you are also using the setting to "format results for Google Data Studio" which overrides any of the formatting special settings. Disable that setting and try again to see if that now displays the dates as expected.